A tiling with triangles and rhombs only

We can dissect the rhomb into triangles and rhombs without using squares. This dissection destroys its mirror-symmetry but leaves the rotational symmetry around its center intact. Together with the dissection of the triangle into rhombs and triangles shown in the last post we get an enantiomorphic tiling without mirror-symmetry. It too has stars of twelve rhombs:

Tiling of twelve-fold rotational symmetry made of triangles and rhombs only.

The larger self-similar structure can only be seen on a larger scale. Note the whirling braided bands of rhombs:

The same tiling as above on a larger scale showing the hierarchical structure of twisting bands of rhombs.

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